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  • Level: GCSE
  • Subject: Maths
  • Word count: 3769

In this investigation I am going to look at the difference between two types of newspaper: tabloids, and broadsheets.

Extracts from this document...

Introduction

Statistics Coursework


Introduction

In this investigation I am going to look at the difference between two types of newspaper: tabloids, and broadsheets.  I could compare the number of letters in a word, the proportion of text to images, but I have chosen to compare the lengths of sentences, as I think broadsheets will have longer sentences on average, as they are more ‘intellectual’ newspapers.  They are not like tabloids that are easy to dip into for news for busy working class people; but are there specifically for people who want to, and have the time to, to read the news fully, and in more depth.  In addition, this will not be too complicated to find out, as, for example, finding the proportion of text to images is more open to error. Again, the tabloid newspaper the wording used is generally less profound and therefore more easily understood.

Plan.

My main aim in this assignment is to prove my hypothesis, below, for the main investigation and the extension task.

I will carry out the task by taking a stratified –systematic sample from both articles. I am going to take a sample size of 38 sentences for two different newspapers, one national tabloid, and one national broadsheet; I’m assuming that all broadsheets and all tabloids are similar. I’ve used a sample size of 38, as it is large enough to be reasonably accurate, whilst not too large that it would take too long to collect the data.

I will have to decide whether on the best way to collect the data, judging on how many sentences the article consists of.   Another sampling method I considered was to count all the sentences in one particular article for each paper, i.e. back page.

...read more.

Middle

 ≤ 60

Frequency

2

1

Cumulative Frequency

37

38

Cumulative Frequency Diagram for the Broadsheet

Now I will construct a Comparative Cumulative Frequency Diagram displaying the two sets of data. This can be found below.

Comparative Cumulative Frequency Diagram displaying the two sets of data.

Now, as the data is in a grouped frequency, the mean is calculated using the midpoints of each group. The midpoints have been calculated in the table below.

Frequency

Mid-Point

0 < w ≤ 10

05

10 < w ≤ 20

15

20 < w ≤ 30

25

30 < w ≤ 40

35

40 < w ≤ 50

45

50 < w ≤ 60

55

The Sun

(5 x 7) + (15 x 7) + (25 x 14) + (35 x 8) + (45 x 2) = 860

38  = A mean of 23 (to 1 d.p.)

Median =  20 < w < 30

Mode =    20 < w < 30

Box and Whisker Plot showing information from the Tabloid.

The Guardian

(5 x 7) + (15 x 9) + (25 x 15) + (35 x 4) + (45 x 2) + (55 x 1) = 830

38 = A mean of 22 (to 1 d.p.)

Median  = 20 < w < 30

Mode  = 20 < w < 30

Box and Whisker Plot showing the data from the Broadsheet.

Comparative Box and Whisker Plot

Mini Conclusion

It is clear that by using grouped data, the Median and Mode fall under the same group for each newspaper. The Braodsheet and Tabloid Data is negatively skewed Also, the mean for the Tabloid is still slightly higher than the Broadsheet, as it was when the data was ungrouped. Also, the sample of sentences from the Sun has a larger mean than the sample taken from the Guardian, suggesting that the sentences, on average are longer in the Sun, however this evidence is not conclusive, so further calculations have to be made.

I will now display a Cumulative frequency Diagram and Box Plot containing both sets of data.

This shows that the Sun has a more consistent sentence length than the Guardian. The Sun has a smaller range and Inter-quartile Range; the cumulative frequency diagram shows the Sun to have a steeper ogive than the Guardian, also suggesting consistency.

Pie Charts

In order for me to construct a pie chart, I will use the following formulae:

                      360(º) / 38 (total sentences) = 9.47, therefore

                                   1º = 9.47 x n = nº

Tabloid

Number of Words

Frequency

Calculation

Degrees on diagram

0 < w ≤ 10

7

7 x 9.47

66.3º

10 < w ≤20

7

7 x 9.47

66.3º

20 < w ≤ 30

14

14 x 9.47

132.63º

30 < w ≤ 40

8

8 x 9.47

75.78º

40 < w ≤ 50

2

2 x 9.47

18.97º

Pie-chart for the tabloid newspaper.

Mini-conclusion

This shows that the modal sentence length is 20 < w ≤ 30. This group is in the middle of the five groups suggesting that the sentence lengths are a consistent value. The remaining four groups prove this, the groups on either side (10 < w ≤20 and 30 < w ≤ 40 slightly lower than the 20 < w ≤ 30 group, and it is true for the other groups.

Below is the table containing the data needed to construct a pie chart for the Broadsheet newspaper.

Broadsheet

Number of Words

Frequency

Calculation

Degrees on diagram

0 < w ≤ 10

7

7 x 9.47

66.3º

10 < w ≤ 20

9

9 x 9.47

85.2º

20 < w ≤ 30

15

15 x 9.47

142.1º

30 < w ≤ 40

4

4 x 9.47

37.8º

40 < w ≤ 50

2

2 x 9.47

18.9º

50 < w ≤ 60

1

1 x 9.47

9.47º

Pie Chart for the Broadsheet’s data.

Mini-conclusion.

Similarly to the previous Chart, the modal sentence length is 20 < w ≤ 30. When compared to the Tabloid, this has one more group, which shows that the broadsheet is not as consistent.

Bar charts and Frequency Polygons

I have decided to construct simple Bar charts along with Frequency polygons. I have collected together the information from each article and constructed simple frequency tables, below.

Tabloid

Number of Words

0 < w ≤ 10

10 < w ≤ 20

20 < w ≤ 30

30 < w ≤ 40

40 < w ≤ 50

Frequency

7

7

14

8

2

Bar chart and frequency polygon for the Tabloid newspaper

Broadsheet

Number of words

0 < w ≤ 10

10 < w ≤ 20

20 < w ≤ 30

30 < w ≤ 40

Frequency

7

9

15

4

Number of Words

40 < w ≤ 50

50 < w ≤ 60

Frequency

2

1

Bar chart and frequency polygon for the broadsheet Newspaper.

Now, to enable me to compare each chart, I will draw the two charts onto one diagram – making it easier to compare.

Comparative Bar Chart and Frequency Polygon

Mini-conclusion.

This shows that the pattern of frequencies in the Sun is more balanced than in the Guardian. The frequency polygon has low frequencies in the low groups and high groups, leaving the middle values with a high frequency.

Histograms.

From the collected data, I will calculate the frequency density to illustrate the dispersion of the data.

To find the frequency density, I will use the following formula:

                Frequency Density =          Frequency

                                          Width of Class Interval

Again I will use grouped frequencies to make the graph more appropriate and less confusing to analyse.

Tabloid

Number of Words

Frequency

Frequency Density

0 < w ≤ 10

7

7 / 10 = 0.7

10 < w ≤ 20

7

7 / 10 = 0.7

20 < w ≤ 30

14

14 / 10 = 1.4

30 < w ≤ 40

8

8 / 10 = 0.8

40 < w ≤ 50

2

2 / 10 = 0.2

...read more.

Conclusion

Finally, I think the Sun was more consistent overall, as the reporters are usually settled into a style of writing. The Guardian used informative detailed language, in comparison to the sun, where the journalist made opinions. This would make the Sun more varied dependant on the thoughts of the person, as he/she would be thinking off the top of their heads rather than structuring an article. It is apparent that the tabloid only briefly comments on the news/articles whereas the broadsheet goes into great depths.

This investigation may not be 100% accurate.  This may be because of many things, I solely was responsible for data collection, and although I checked for mistakes, many may have been overlooked.  A disadvantage that I had was that I only looked at one tabloid and one broadsheet.  The newspapers that I selected may not be typical of those kinds of paper, so it would have been an advantage to sample more papers.  If I were to repeat this investigation, or extend it I would sample more newspapers, however it was not possible to do it this time because it would be so time-consuming.  If it were feasible to collect data like this for many samples, then I’d plot an accurate graph for the means of the means of the sample, which would be normally distributed, as long as the sample were large enough – The Central Limit Theorem states that ‘If the sample size is large enough then the distribution of the sample means is approximately Normal, irrespective of the distribution of the parent population.’  It would then be easier to predict more accurately the mean of the data.  

Daniel Flynn        11’0        Math Coursework

...read more.

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